Finite Group Databasebeta

← C2×#10594293 #11902416

Subgroups — C2×#10594293 #11902416

Order 1152.

4131 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3811C211yesmaximal, characteristic, complemented
2C22×#3804C211yesmaximal, characteristic, complemented
3C2×#64091C211yesmaximal, characteristic, complemented
4C2×C3×#886C211yesmaximal, characteristic, complemented
5C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
6C2×#63978C211yesmaximal, characteristic, complemented
7C22×#3722C211yesmaximal, characteristic, complemented
8C2×#63923C211yesmaximal, characteristic, complemented
9C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10C2×#63910C211yesmaximal, characteristic, complemented
11C2×#63909C211yesmaximal, characteristic, complemented
12C2×#63895C211yesmaximal, characteristic, complemented
13C2×#63894C211yesmaximal, characteristic, complemented
14C2×#63890C211yesmaximal, characteristic, complemented
15C2×#63852C211yesmaximal, characteristic, complemented
16#10594293C2116yesmaximal, direct product factor
17C2×#5654—31nomaximal
18C2×#5554—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C22×#638C2211yescharacteristic, complemented
22C22×C4⋊(C3⋊D3)C2211yescharacteristic
23C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic
26C23×C3×Dic3C2211yescharacteristic, complemented
27C23×C3×Dic3C2211yescharacteristic, complemented
28C22×C3×C4×D3C2211yescharacteristic, complemented
29C2×#3811—28no—
30C2×#3811C2218yescomplemented
31C22×#627C2211yescharacteristic, complemented
32C22×#626C2211yescharacteristic
33C22×#626C2211yescharacteristic
34C22×#626C2211yescharacteristic, complemented
35C22×#626C2211yescharacteristic, complemented
36C22×#624C2211yescharacteristic
37C22×#624C2211yescharacteristic, complemented
38C2×#3804—28no—
39C2×#3804C2218yescomplemented
40C22×D3×Dic3C2211yescharacteristic, complemented
41C2×C32×C22⋊C4C2211yescharacteristic, complemented
42C2×#3752C2211yescharacteristic
43C2×#3752C2211yescharacteristic, complemented
44#64091C2218yescomplemented
45C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
49C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
50C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
51C2×C3×C4×Dic3C2211yescharacteristic, complemented
52C3×#886C2218yescomplemented
53C3×#67⋊C4C2218yescomplemented
54#63978C2218yescomplemented
55C2×Dic3⋊Dic3C2211yescharacteristic, complemented
56C2×#3722C2211yescharacteristic
57C2×#3722C2211yescharacteristic
58C2×#3722C2218yescomplemented
59C2×#3722C2211yescharacteristic, complemented
60C2×#3722C2211yescharacteristic, complemented
61C2×#3722C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63#63923C2218yescomplemented
64D3×(C2×D3)⋊C4C2218yescomplemented
65#63910C2218yescomplemented
66#63909C2218yescomplemented
67#63895C2218yescomplemented
68#63894C2218yescomplemented
69#63890C2218yescomplemented
70#63852C2218yescomplemented
71C22×#237—31no—
72C22×D3×D4—31no—
73C22×D3×D4—31no—
74C22×#235—31no—
75C2×C3×#123—31no—
76C2×C3×C4×D4—31no—
77C2×#939—31no—
78C2×#930—31no—
79C2×#930—31no—
80C22×(C2×D3)⋊C4—31no—
81C22×(C2×D3)⋊C4—31no—
82C22×(C2×D3)⋊C4—31no—
83#5654—316no—
84#5554—316no—
85C2×#897—31no—
86C2×#896—31no—
87C2×#895—31no—
88C2×#895—31no—
89C2×#894—31no—
90C2×#893—31no—
91C2×#886—31no—
92C2×#886D311yescharacteristic, complemented
93C2×#885—31no—
94C2×#884—31no—
95C2×#882—31no—
96C2×#882—31no—
97C2×#882—31no—
98C2×#882—31no—
99C2×#882—61no—
100C2×#67⋊C4D311yescharacteristic, complemented
101C2×D3×C22⋊C4—31no—
102C2×#875—31no—
103C2×C4×D12—31no—
104C24×C32C2311yescharacteristic
105C23×C3⋊D3—24no—
106C23×C3⋊D3—24no—
107C23×C3⋊D3—42no—
108C23×C3⋊D3C2311yescharacteristic
109C23×C3⋊D3C2311yescharacteristic
110C23×C3⋊D3C2314yes—
111C23×C3⋊D3C2311yescharacteristic
112C23×C3×D3C2311yescharacteristic
113C23×C3×D3C2311yescharacteristic
114C22×D32—24no—
115C22×D32—24no—
116C22×D32—42no—
117C22×D32C2314yes—
118C22×C32×C4C2311yescharacteristic
119C22×C32×C4C2311yescharacteristic
120C2×#638—24no—
121C2×#638C2314yescomplemented
122C22×C3⋊Dic3C2311yescharacteristic
123C2×C4⋊(C3⋊D3)—24no—
124C2×C4⋊(C3⋊D3)—42no—
125C2×C4⋊(C3⋊D3)C2314yes—
126C2×C4⋊(C3⋊D3)C2314yescomplemented
127C2×C3×#67—24no—
128C2×C3×#67D418yescomplemented
129C2×C3×#67C2314yes—
130C2×C3×#67C2314yes—
131C22×C3×Dic3—24no—
132C22×C3×Dic3—42no—
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2311yescharacteristic
137C22×C3×Dic3C2311yescharacteristic
138C22×C3×Dic3C2311yescharacteristic
139C22×C3×Dic3C2314yescomplemented
140C22×C3×Dic3C2314yescomplemented
141C2×C3×C4×D3—42no—
142C2×C3×C4×D3C2314yescomplemented
143#3811—232no—
144C2×#627—24no—
145C2×#627C2314yescomplemented
146C2×#626—24no—
147C2×#626—24no—
148C2×#626—24no—
149C2×#626—42no—
150C2×#626C2314yes—
151C2×#626C2314yes—
152C2×#626C2314yescomplemented
153C2×#626C2314yescomplemented
154C2×#624—24no—
155C2×#624—24no—
156C2×#624C2314yes—
157C2×#624C2314yescomplemented
158#3804—232no—
159C2×D3×Dic3—24no—
160C2×D3×Dic3C2314yescomplemented
161C32×C22⋊C4C2314yescomplemented
162#3752C2314yes—
163#3752C2314yescomplemented
164C3×(C2×D3)⋊C4C2314yescomplemented
165C3×(C2×D3)⋊C4C2314yescomplemented
166C3×(C2×D3)⋊C4C2314yescomplemented
167C3×C4⋊Dic3C2314yescomplemented
168C3×C4⋊Dic3C2314yescomplemented
169C3×Dic3⋊C4C2314yescomplemented
170C3×C4×Dic3C2314yescomplemented
171Dic3⋊Dic3C2314yescomplemented
172#3722C2314yes—
173#3722C2314yes—
174#3722C2314yescomplemented
175#3722C2314yescomplemented
176#3722C2314yescomplemented
177(C2×D3)⋊Dic3C2314yescomplemented
178C2×#546—91noSylow
179C24×D3—31no—
180C24×D3—31no—
181C24×D3—31no—
182C24×D3—31no—
183C24×D3—61no—
184C22×C3×D4—31no—
185C22×C3×D4—31no—
186C23×C3×C4—31no—
187C23×C3×C4—31no—
188C23×C3×C4—31no—
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—31no—
195C22×#67—61no—
196C22×#67C2×D311yescharacteristic
197C22×#67C2×D311yescharacteristic
198C23×Dic3—31no—
199C23×Dic3C2×D311yescharacteristic, complemented
200C23×Dic3C2×D311yescharacteristic, complemented
201C2×#237—38no—
202C2×#237—68no—
203C2×D3×D4—38no—
204C2×D3×D4—38no—
205C2×D3×D4—68no—
206C2×D3×D4—68no—
207C2×#235—38no—
208C2×#235—68no—
209C22×D12—31no—
210C22×D12—31no—
211C22×D12—31no—
212C22×D12—31no—
213C22×D12—31no—
214C22×D12—31no—
215C22×D12—31no—
216C22×D12—31no—
217C22×D12—61no—
218C22×D12—61no—
219C22×C4×D3—31no—
220C22×C4×D3—31no—
221C22×C4×D3—31no—
222C22×C4×D3—31no—
223C22×C4×D3—31no—
224C22×C4×D3C2×D311yescharacteristic, complemented
225C22×Dic6—31no—
226C22×Dic6—31no—
227C3×#123—38no—
228C3×C4×D4—38no—
229C2×C3×C4⋊C4—31no—
230C2×C3×C4⋊C4—31no—
231C2×C3×C4⋊C4—31no—
232C2×C3×C22⋊C4—21no—
233C2×C3×C22⋊C4—31no—
234C2×C3×C22⋊C4—31no—
235C2×C3×C22⋊C4—31no—
236C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
237C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
238C2×C3×C42—31no—
239C2×#217—31no—
240#939—38no—
241#930—38no—
242#930—38no—
243C2×(C2×D3)⋊C4—31no—
244C2×(C2×D3)⋊C4—31no—
245C2×(C2×D3)⋊C4—31no—
246C2×(C2×D3)⋊C4—31no—
247C2×(C2×D3)⋊C4—31no—
248C2×(C2×D3)⋊C4—31no—
249C2×(C2×D3)⋊C4—31no—
250C2×(C2×D3)⋊C4—31no—
251C2×(C2×D3)⋊C4—31no—
252C2×(C2×D3)⋊C4—31no—
253C2×(C2×D3)⋊C4—31no—
254C2×(C2×D3)⋊C4—31no—
255C2×(C2×D3)⋊C4—31no—
256C2×(C2×D3)⋊C4—31no—
257C2×(C2×D3)⋊C4—31no—
258C2×(C2×D3)⋊C4—38no—
259C2×(C2×D3)⋊C4—38no—
260C2×(C2×D3)⋊C4—38no—
261C2×(C2×D3)⋊C4—61no—
262C2×(C2×D3)⋊C4—61no—
263C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
264C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
265C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
266C2×C4⋊Dic3—31no—
267C2×C4⋊Dic3C2×D311yescharacteristic, complemented
268C2×C4⋊Dic3C2×D311yescharacteristic, complemented
269C2×Dic3⋊C4—31no—
270C2×Dic3⋊C4C2×D311yescharacteristic, complemented
271C2×C4×Dic3C2×D311yescharacteristic, complemented
272#897—38no—
273#896—38no—
274#895—38no—
275#895—38no—
276#894—38no—
277#893—38no—
278#886—38no—
279#886C2×D318yescomplemented
280#885—38no—
281#884—38no—
282#882—38no—
283#882—38no—
284#882—38no—
285#882—38no—
286#882—68no—
287#67⋊C4C2×D318yescomplemented
288D3×C22⋊C4—38no—
289#875—38no—
290C4×D12—38no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32C2×D414yes—
294C23×C32C2412yes—
295C23×C32C2411yescharacteristic
296C22×C3⋊D3—22no—
297C22×C3⋊D3—22no—
298C22×C3⋊D3—22no—
299C22×C3⋊D3—22no—
300C22×C3⋊D3—28no—
301C22×C3⋊D3—22no—
302C22×C3⋊D3—22no—
303C22×C3⋊D3—22no—
304C22×C3⋊D3—22no—
305C22×C3⋊D3—28no—
306C22×C3⋊D3—44no—
307C22×C3⋊D3—416no—
308C22×C3⋊D3#4114yescomplemented
309C22×C3⋊D3C2412yes—
310C22×C3⋊D3C2412yes—
311C22×C3⋊D3C2412yes—
312C22×C3×D3—22no—
313C22×C3×D3—22no—
314C22×C3×D3—22no—
315C22×C3×D3—22no—
316C22×C3×D3—22no—
317C22×C3×D3C2×D414yes—
318C22×C3×D3C2412yes—
319C22×C3×D3C2412yes—
320C2×D32—28no—
321C2×D32—28no—
322C2×D32—44no—
323C2×D32—416no—
324C2×C32×C4—22no—
325C2×C32×C4—22no—
326C2×C32×C4C2412yes—
327C2×C32×C4C2412yes—
328#638—28no—
329C2×C3⋊Dic3—22no—
330C2×C3⋊Dic3C2412yes—
331C4⋊(C3⋊D3)—28no—
332C4⋊(C3⋊D3)—44no—
333C3×#67—28no—
334C3×#67C2×D4116yescomplemented
335C2×C3×Dic3—22no—
336C2×C3×Dic3—28no—
337C2×C3×Dic3—22no—
338C2×C3×Dic3—22no—
339C2×C3×Dic3—22no—
340C2×C3×Dic3—22no—
341C2×C3×Dic3—44no—
342C2×C3×Dic3C2×D414yes—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C3×C4×D3—44no—
350#627—28no—
351#626—28no—
352#626—28no—
353#626—28no—
354#626—44no—
355#624—28no—
356#624—28no—
357D3×Dic3—28no—
358C22×#41—91no—
359C23×D4—91no—
360#546—916no—
361C2×#124—91no—
362C2×#123—31no—
363C2×#123—91no—
364C2×C22⋊Q8—91no—
365C2×#121—91no—
366C2×#121—91no—
367C2×#121—91no—
368C2×#120—91no—
369C2×#120—91no—
370C2×C4×D4—31no—
371C2×C4×D4—91no—
372C22×C22⋊C4—91no—
373C22×C22⋊C4—91no—
374C24×C3—21no—
375C24×C3—31no—
376C24×C3—31no—
377C24×C3C22×D311yescharacteristic
378C24×C3C22×D311yescharacteristic
379C23×D3—31no—
380C23×D3—31no—
381C23×D3—31no—
382C23×D3—31no—
383C23×D3—31no—
384C23×D3—31no—
385C23×D3—34no—
386C23×D3—34no—
387C23×D3—34no—
388C23×D3—34no—
389C23×D3—61no—
390C23×D3—61no—
391C23×D3—64no—
392C23×D3—61no—
393C23×D3—64no—
394C23×D3—64no—
395C23×D3—64no—
396C23×D3—64no—
397C23×D3—64no—
398C23×D3—64no—
399C23×D3—64no—
400C23×D3—64no—
401C23×D3—124no—
402C23×D3—124no—
403C23×D3—122no—
404C23×D3—122no—
405C23×D3—122no—
406C23×D3—122no—
407C23×D3—124no—
408C23×D3C22×D311yescharacteristic
409C23×D3C22×D311yescharacteristic
410C2×C3×D4—38no—
411C2×C3×D4—34no—
412C2×C3×D4—34no—
413C2×C3×D4—64no—
414C22×C3×C4—21no—
415C22×C3×C4—21no—
416C22×C3×C4—31no—
417C22×C3×C4—31no—
418C22×C3×C4—31no—
419C22×C3×C4—31no—
420C22×C3×C4—31no—
421C22×C3×C4—31no—
422C22×C3×C4—34no—
423C22×C3×C4—34no—
424C22×C3×C4—34no—
425C22×C3×C4—64no—
426C22×C3×C4—122no—
427C22×C3×C4—122no—
428C22×C3×C4C22×D311yescharacteristic
429C22×C3×C4C22×D311yescharacteristic
430C22×C3×C4C22×D311yescharacteristic
431C22×C3×C4C22×D311yescharacteristic
432C2×#67—24no—
433C2×#67—34no—
434C2×#67—34no—
435C2×#67—34no—
436C2×#67—34no—
437C2×#67—34no—
438C2×#67—34no—
439C2×#67—64no—
440C2×#67—64no—
441C2×#67—64no—
442C2×#67—64no—
443C2×#67—64no—
444C2×#67—64no—
445C2×#67—124no—
446C2×#67—122no—
447C2×#67D1218yescomplemented
448C2×#67C22×D314yes—
449C2×#67C22×D314yes—
450C22×Dic3—24no—
451C22×Dic3—31no—
452C22×Dic3—31no—
453C22×Dic3—34no—
454C22×Dic3—42no—
455C22×Dic3—61no—
456C22×Dic3—64no—
457C22×Dic3C22×D311yescharacteristic
458C22×Dic3C22×D311yescharacteristic
459C22×Dic3C22×D311yescharacteristic
460C22×Dic3C22×D311yescharacteristic
461C22×Dic3C22×D311yescharacteristic
462C22×Dic3C22×D311yescharacteristic
463C22×Dic3C22×D314yescomplemented
464C22×Dic3C22×D314yescomplemented
465#237—632no—
466D3×D4—632no—
467D3×D4—632no—
468#235—632no—
469C2×D12—34no—
470C2×D12—34no—
471C2×D12—34no—
472C2×D12—34no—
473C2×D12—34no—
474C2×D12—34no—
475C2×D12—34no—
476C2×D12—34no—
477C2×D12—64no—
478C2×D12—64no—
479C2×D12—64no—
480C2×D12—64no—
481C2×D12—64no—
482C2×D12—64no—
483C2×D12—64no—
484C2×D12—124no—
485C2×D12—122no—
486C2×D12—122no—
487C2×D12—124no—
488C2×D12—122no—
489C2×C4×D3—34no—
490C2×C4×D3—34no—
491C2×C4×D3—34no—
492C2×C4×D3—34no—
493C2×C4×D3—34no—
494C2×C4×D3—42no—
495C2×C4×D3—64no—
496C2×C4×D3—64no—
497C2×C4×D3—64no—
498C2×C4×D3—64no—
499C2×C4×D3—64no—
500C2×C4×D3C22×D314yescomplemented
501C2×Dic6—34no—
502C2×Dic6—34no—
503C2×Dic6—64no—
504C2×Dic6—64no—
505C3×C4⋊C4—34no—
506C3×C4⋊C4—34no—
507C3×C4⋊C4—34no—
508C3×C22⋊C4—24no—
509C3×C22⋊C4—34no—
510C3×C22⋊C4—34no—
511C3×C22⋊C4—34no—
512C3×C22⋊C4C22×D314yescomplemented
513C3×C22⋊C4C22×D314yescomplemented
514C3×C42—34no—
515#217—34no—
516(C2×D3)⋊C4—34no—
517(C2×D3)⋊C4—34no—
518(C2×D3)⋊C4—34no—
519(C2×D3)⋊C4—34no—
520(C2×D3)⋊C4—34no—
521(C2×D3)⋊C4—34no—
522(C2×D3)⋊C4—34no—
523(C2×D3)⋊C4—34no—
524(C2×D3)⋊C4—34no—
525(C2×D3)⋊C4—34no—
526(C2×D3)⋊C4—34no—
527(C2×D3)⋊C4—34no—
528(C2×D3)⋊C4—34no—
529(C2×D3)⋊C4—34no—
530(C2×D3)⋊C4—34no—
531(C2×D3)⋊C4—64no—
532(C2×D3)⋊C4—64no—
533(C2×D3)⋊C4C22×D314yescomplemented
534(C2×D3)⋊C4C22×D314yescomplemented
535(C2×D3)⋊C4C22×D314yescomplemented
536C4⋊Dic3—34no—
537C4⋊Dic3C22×D314yescomplemented
538C4⋊Dic3C22×D314yescomplemented
539Dic3⋊C4—34no—
540Dic3⋊C4C22×D314yescomplemented
541C4×Dic3C22×D314yescomplemented
542C22×C32—28no—
543C22×C32—22no—
544C22×C32—22no—
545C22×C32C22×D414yes—
546C22×C32C22×D412yes—
547C22×C32C2×#4112yes—
548C22×C32H(5,𝔽2)12yes—
549C22×C32C2511yescharacteristic
550C2×C3⋊D3—22no—
551C2×C3⋊D3—28no—
552C2×C3⋊D3—22no—
553C2×C3⋊D3—22no—
554C2×C3⋊D3—22no—
555C2×C3⋊D3—22no—
556C2×C3⋊D3—22no—
557C2×C3⋊D3—22no—
558C2×C3⋊D3—22no—
559C2×C3⋊D3—416no—
560C2×C3⋊D3—44no—
561C2×C3⋊D3—44no—
562C2×C3⋊D3C2×#4114yescomplemented
563C2×C3×D3—28no—
564C2×C3×D3—22no—
565C2×C3×D3—22no—
566C2×C3×D3—22no—
567C2×C3×D3—22no—
568C2×C3×D3—22no—
569C2×C3×D3—44no—
570C2×C3×D3C22×D414yes—
571D32—416no—
572C32×C4—22no—
573C32×C4—22no—
574C3⋊Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3—22no—
577C3×Dic3—22no—
578C3×Dic3—22no—
579C3×Dic3—22no—
580C3×Dic3C22×D414yes—
581C25—91no—
582C25—91no—
583C2×#41—98no—
584C2×#41—188no—
585C22×Q8—91no—
586C22×D4—31no—
587C22×D4—31no—
588C22×D4—91no—
589C22×D4—91no—
590C22×D4—91no—
591C22×D4—91no—
592C22×D4—98no—
593C22×D4—91no—
594C22×D4—91no—
595C22×D4—91no—
596C22×D4—188no—
597C23×C4—31no—
598C23×C4—31no—
599C23×C4—31no—
600C23×C4—91no—
601C23×C4—91no—
602C23×C4—91no—
603#124—98no—
604#123—38no—
605#123—98no—
606C22⋊Q8—98no—
607#121—98no—
608#121—98no—
609#121—98no—
610#120—98no—
611#120—98no—
612C4×D4—38no—
613C4×D4—98no—
614C2×C4⋊C4—31no—
615C2×C4⋊C4—31no—
616C2×C4⋊C4—31no—
617C2×C4⋊C4—91no—
618C2×C22⋊C4—31no—
619C2×C22⋊C4—31no—
620C2×C22⋊C4—31no—
621C2×C22⋊C4—98no—
622C2×C22⋊C4—91no—
623C2×C22⋊C4—91no—
624C2×C22⋊C4—91no—
625C2×C22⋊C4—91no—
626C2×C22⋊C4—98no—
627C2×C22⋊C4—91no—
628C2×C22⋊C4—91no—
629C2×C22⋊C4—91no—
630C2×C22⋊C4—91no—
631C2×C22⋊C4D3211yescharacteristic, complemented
632C2×C42—31no—
633C23×C3—22no—
634C23×C3—22no—
635C23×C3—22no—
636C23×C3—22no—
637C23×C3—22no—
638C23×C3—21no—
639C23×C3—24no—
640C23×C3—34no—
641C23×C3—32no—
642C23×C3—32no—
643C23×C3—42no—
644C23×C3—42no—
645C23×C3—62no—
646C23×C3—62no—
647C23×C3—62no—
648C23×C3—62no—
649C23×C3—62no—
650C23×C3C2×D1214yes—
651C23×C3D3×D414yes—
652C23×C3C23×D312yes—
653C23×C3C23×D312yes—
654C23×C3C23×D311yescharacteristic
655C23×C3C23×D311yescharacteristic
656C22×D3—22no—
657C22×D3—22no—
658C22×D3—22no—
659C22×D3—22no—
660C22×D3—22no—
661C22×D3—34no—
662C22×D3—34no—
663C22×D3—32no—
664C22×D3—32no—
665C22×D3—32no—
666C22×D3—32no—
667C22×D3—32no—
668C22×D3—32no—
669C22×D3—64no—
670C22×D3—62no—
671C22×D3—62no—
672C22×D3—62no—
673C22×D3—68no—
674C22×D3—68no—
675C22×D3—68no—
676C22×D3—68no—
677C22×D3—68no—
678C22×D3—62no—
679C22×D3—62no—
680C22×D3—62no—
681C22×D3—62no—
682C22×D3—64no—
683C22×D3—62no—
684C22×D3—62no—
685C22×D3—68no—
686C22×D3—62no—
687C22×D3—62no—
688C22×D3—68no—
689C22×D3—62no—
690C22×D3—62no—
691C22×D3—62no—
692C22×D3—62no—
693C22×D3—62no—
694C22×D3—62no—
695C22×D3—62no—
696C22×D3—62no—
697C22×D3—68no—
698C22×D3—128no—
699C22×D3—122no—
700C22×D3—122no—
701C22×D3—122no—
702C22×D3—128no—
703C22×D3—122no—
704C22×D3—122no—
705C22×D3—122no—
706C22×D3—122no—
707C22×D3—124no—
708C22×D3—124no—
709C22×D3—1216no—
710C22×D3—1216no—
711C22×D3—124no—
712C22×D3—124no—
713C22×D3—1216no—
714C22×D3—1216no—
715C22×D3—128no—
716C22×D3—1232no—
717C22×D3C2×D1214yes—
718C22×D3C23×D312yes—
719C22×D3C23×D312yes—
720C3×D4—316no—
721C3×D4—68no—
722C2×C3×C4—22no—
723C2×C3×C4—22no—
724C2×C3×C4—22no—
725C2×C3×C4—22no—
726C2×C3×C4—22no—
727C2×C3×C4—22no—
728C2×C3×C4—34no—
729C2×C3×C4—32no—
730C2×C3×C4—32no—
731C2×C3×C4—32no—
732C2×C3×C4—32no—
733C2×C3×C4—32no—
734C2×C3×C4—32no—
735C2×C3×C4—42no—
736C2×C3×C4—42no—
737C2×C3×C4—62no—
738C2×C3×C4—62no—
739C2×C3×C4—62no—
740C2×C3×C4—68no—
741C2×C3×C4—62no—
742C2×C3×C4—62no—
743C2×C3×C4—124no—
744C2×C3×C4—124no—
745C2×C3×C4C23×D312yes—
746C2×C3×C4C23×D312yes—
747C2×C3×C4C23×D312yes—
748C2×C3×C4C23×D312yes—
749#67—28no—
750#67—68no—
751#67—68no—
752#67—68no—
753#67—68no—
754#67—68no—
755#67—128no—
756#67—124no—
757#67C2×D12116yescomplemented
758C2×Dic3—22no—
759C2×Dic3—22no—
760C2×Dic3—22no—
761C2×Dic3—28no—
762C2×Dic3—22no—
763C2×Dic3—22no—
764C2×Dic3—32no—
765C2×Dic3—32no—
766C2×Dic3—44no—
767C2×Dic3—62no—
768C2×Dic3—68no—
769C2×Dic3—62no—
770C2×Dic3—62no—
771C2×Dic3—122no—
772C2×Dic3C2×D1214yes—
773C2×Dic3C23×D312yes—
774C2×Dic3C23×D312yes—
775C2×Dic3C23×D312yes—
776C2×Dic3C23×D312yes—
777C2×Dic3C23×D312yes—
778C2×Dic3C23×D312yes—
779D12—68no—
780D12—68no—
781D12—68no—
782D12—68no—
783D12—68no—
784D12—128no—
785D12—124no—
786D12—124no—
787D12—128no—
788D12—124no—
789C4×D3—44no—
790C4×D3—68no—
791C4×D3—68no—
792C4×D3—68no—
793C4×D3—68no—
794C4×D3—68no—
795Dic6—68no—
796Dic6—68no—
797C2×C32—24no—
798C2×C32#54614yescomplemented
799C2×C32C23×D411yescharacteristic
800C2×C32C22×#4111yescharacteristic
801C2×C32C2×H(5,𝔽2)11yescharacteristic
802C3⋊D3—24no—
803C3⋊D3—42no—
804C3⋊D3—42no—
805C3×D3—24no—
806C3×D3—42no—
807C24—31no—
808C24—31no—
809C24—94no—
810C24—91no—
811C24—91no—
812C24—91no—
813C24—94no—
814C24—184no—
815C24—184no—
816C24—184no—
817C24—184no—
818C24—362no—
819C24—362no—
820C24C2×D3211yescharacteristic
821#41—1832no—
822C2×Q8—94no—
823C2×Q8—184no—
824C2×D4—34no—
825C2×D4—38no—
826C2×D4—34no—
827C2×D4—64no—
828C2×D4—94no—
829C2×D4—94no—
830C2×D4—94no—
831C2×D4—94no—
832C2×D4—94no—
833C2×D4—94no—
834C2×D4—94no—
835C2×D4—184no—
836C2×D4—184no—
837C2×D4—184no—
838C2×D4—184no—
839C2×D4—1832no—
840C2×D4—184no—
841C2×D4—362no—
842C2×D4—362no—
843C22×C4—31no—
844C22×C4—34no—
845C22×C4—31no—
846C22×C4—31no—
847C22×C4—31no—
848C22×C4—31no—
849C22×C4—31no—
850C22×C4—34no—
851C22×C4—34no—
852C22×C4—64no—
853C22×C4—94no—
854C22×C4—94no—
855C22×C4—94no—
856C22×C4—91no—
857C22×C4—122no—
858C22×C4—122no—
859C22×C4—184no—
860C22×C4—184no—
861C22×C4—184no—
862C22×C4C2×D3211yescharacteristic
863C22×C4C2×D3211yescharacteristic
864C4⋊C4—34no—
865C4⋊C4—34no—
866C4⋊C4—34no—
867C4⋊C4—94no—
868C22⋊C4—34no—
869C22⋊C4—34no—
870C22⋊C4—34no—
871C22⋊C4—94no—
872C22⋊C4—94no—
873C22⋊C4—94no—
874C22⋊C4—94no—
875C22⋊C4—94no—
876C22⋊C4—94no—
877C22⋊C4—94no—
878C22⋊C4—94no—
879C22⋊C4C2×D3214yescomplemented
880C42—34no—
881C22×C3—28no—
882C22×C3—22no—
883C22×C3—22no—
884C22×C3—22no—
885C22×C3—22no—
886C22×C3—28no—
887C22×C3—22no—
888C22×C3—24no—
889C22×C3—22no—
890C22×C3—22no—
891C22×C3—21no—
892C22×C3—34no—
893C22×C3—42no—
894C22×C3—42no—
895C22×C3—48no—
896C22×C3—68no—
897C22×C3—62no—
898C22×C3—62no—
899C22×C3—62no—
900C22×C3—62no—
901C22×C3—62no—
902C22×C3—124no—
903C22×C3C22×D1214yes—
904C22×C3C22×D1212yes—
905C22×C3C2×D3×D414yes—
906C22×C3C2×D3×D412yes—
907C22×C3#100412yes—
908C22×C3D3×#4112yes—
909C22×C3D3×#4112yes—
910C22×C3#100912yes—
911C22×C3C24×D311yescharacteristic
912C22×C3C24×D311yescharacteristic
913C2×D3—22no—
914C2×D3—22no—
915C2×D3—28no—
916C2×D3—22no—
917C2×D3—22no—
918C2×D3—22no—
919C2×D3—34no—
920C2×D3—34no—
921C2×D3—44no—
922C2×D3—64no—
923C2×D3—68no—
924C2×D3—62no—
925C2×D3—62no—
926C2×D3—62no—
927C2×D3—62no—
928C2×D3—68no—
929C2×D3—64no—
930C2×D3—62no—
931C2×D3—62no—
932C2×D3—62no—
933C2×D3—62no—
934C2×D3—62no—
935C2×D3—62no—
936C2×D3—62no—
937C2×D3—62no—
938C2×D3—62no—
939C2×D3—62no—
940C2×D3—62no—
941C2×D3—62no—
942C2×D3—122no—
943C2×D3—122no—
944C2×D3—128no—
945C2×D3—122no—
946C2×D3—122no—
947C2×D3—122no—
948C2×D3—122no—
949C2×D3—122no—
950C2×D3—1216no—
951C2×D3—1216no—
952C2×D3—1216no—
953C2×D3—1216no—
954C2×D3—128no—
955C2×D3—1232no—
956C2×D3—124no—
957C2×D3—124no—
958C2×D3—124no—
959C2×D3—124no—
960C2×D3—244no—
961C2×D3C22×D1214yes—
962C3×C4—22no—
963C3×C4—22no—
964C3×C4—22no—
965C3×C4—22no—
966C3×C4—34no—
967C3×C4—42no—
968C3×C4—42no—
969C3×C4—62no—
970C3×C4—62no—
971C3×C4—62no—
972C3×C4—62no—
973C3×C4—62no—
974Dic3—22no—
975Dic3—22no—
976Dic3—22no—
977Dic3—22no—
978Dic3—22no—
979Dic3—62no—
980Dic3—62no—
981Dic3—122no—
982Dic3C22×D1214yes—
983C32C2×#54611yescharacteristic, complemented, Sylow
984C23—22no—
985C23—22no—
986C23—34no—
987C23—32no—
988C23—32no—
989C23—62no—
990C23—62no—
991C23—62no—
992C23—62no—
993C23—62no—
994C23—94no—
995C23—92no—
996C23—92no—
997C23—92no—
998C23—188no—
999C23—188no—
1000C23—188no—
1001C23—182no—
1002C23—182no—
1003C23—182no—
1004C23—188no—
1005C23—182no—
1006C23—182no—
1007C23—182no—
1008C23—182no—
1009C23—182no—
1010C23—364no—
1011C23—3616no—
1012C23—364no—
1013C23—3616no—
1014C23D3×D1214yes—
1015C23C22×D3212yes—
1016C23C22×D3211yescharacteristic
1017Q8—188no—
1018D4—316no—
1019D4—68no—
1020D4—188no—
1021D4—188no—
1022D4—188no—
1023D4—188no—
1024D4—188no—
1025D4—364no—
1026D4—364no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—34no—
1030C2×C4—32no—
1031C2×C4—32no—
1032C2×C4—32no—
1033C2×C4—32no—
1034C2×C4—32no—
1035C2×C4—32no—
1036C2×C4—62no—
1037C2×C4—62no—
1038C2×C4—68no—
1039C2×C4—62no—
1040C2×C4—62no—
1041C2×C4—62no—
1042C2×C4—92no—
1043C2×C4—124no—
1044C2×C4—124no—
1045C2×C4—188no—
1046C2×C4—188no—
1047C2×C4—188no—
1048C2×C4—182no—
1049C2×C4C22×D3212yes—
1050C2×C4C22×D3212yes—
1051C2×C3—24no—
1052C2×C3—24no—
1053C2×C3—21no—
1054C2×C3—21no—
1055C2×C3—21no—
1056C2×C3—24no—
1057C2×C3—44no—
1058C2×C3—64no—
1059C2×C3—122no—
1060C2×C3#555414yescomplemented
1061C2×C3#565414yescomplemented
1062C2×C3C23×D1211yescharacteristic
1063C2×C3C22×D3×D411yescharacteristic
1064C2×C3C2×#100411yescharacteristic
1065C2×C3C2×D3×#4111yescharacteristic
1066C2×C3C2×D3×#4111yescharacteristic
1067C2×C3C2×#100911yescharacteristic
1068D3—24no—
1069D3—42no—
1070D3—64no—
1071D3—64no—
1072D3—124no—
1073D3—124no—
1074D3—122no—
1075D3—122no—
1076D3—122no—
1077D3—122no—
1078D3—242no—
1079C22—22no—
1080C22—22no—
1081C22—28no—
1082C22—34no—
1083C22—62no—
1084C22—62no—
1085C22—68no—
1086C22—62no—
1087C22—62no—
1088C22—62no—
1089C22—94no—
1090C22—124no—
1091C22—182no—
1092C22—182no—
1093C22—188no—
1094C22—182no—
1095C22—182no—
1096C22—182no—
1097C22—182no—
1098C22—182no—
1099C22—182no—
1100C22—3616no—
1101C22—3616no—
1102C22—364no—
1103C22—364no—
1104C22C2×D3×D1214yes—
1105C22C2×D3×D1212yes—
1106C22#6431212yes—
1107C22#6431412yes—
1108C22C23×D3211yescharacteristic
1109C4—22no—
1110C4—22no—
1111C4—34no—
1112C4—62no—
1113C4—62no—
1114C4—62no—
1115C4—62no—
1116C4—62no—
1117C4—182no—
1118C3—21no—
1119C3C2×#555411yescharacteristic, complemented
1120C3C2×#565411yescharacteristic, complemented
1121C2—24no—
1122C2—64no—
1123C2—122no—
1124C2—184no—
1125C2—362no—
1126C2—362no—
1127C2#1059429314yesdirect product factor
1128C2C22×D3×D1211yescharacteristic
1129C2C2×#6431211yescharacteristic
1130C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#3811C2semidirect
2. C22×#3804C2semidirect
3. C2×#64091C2semidirect
4. C2×C3×#886C2semidirect
5. C2×C3×#67⋊C4C2semidirect
6. C2×#63978C2semidirect
7. C22×#3722C2semidirect
8. C2×#63923C2semidirect
9. C2×D3×(C2×D3)⋊C4C2semidirect
10. C2×#63910C2semidirect
11. C2×#63909C2semidirect
12. C2×#63895C2semidirect
13. C2×#63894C2semidirect
14. C2×#63890C2semidirect
15. C2×#63852C2semidirect
16. #10594293C2direct (N × H)
21. C22×#638C22semidirect
23. C22×C4⋊(C3⋊D3)C22semidirect
26. C23×C3×Dic3C22semidirect
27. C23×C3×Dic3C22semidirect
28. C22×C3×C4×D3C22semidirect
30. C2×#3811C22semidirect
31. C22×#627C22semidirect
34. C22×#626C22semidirect
35. C22×#626C22semidirect
37. C22×#624C22semidirect
39. C2×#3804C22semidirect
40. C22×D3×Dic3C22semidirect
41. C2×C32×C22⋊C4C22semidirect
43. C2×#3752C22semidirect
44. #64091C22semidirect
45. C2×C3×(C2×D3)⋊C4C22semidirect
46. C2×C3×(C2×D3)⋊C4C22semidirect
47. C2×C3×(C2×D3)⋊C4C22semidirect
48. C2×C3×C4⋊Dic3C22semidirect
49. C2×C3×C4⋊Dic3C22semidirect
50. C2×C3×Dic3⋊C4C22semidirect
51. C2×C3×C4×Dic3C22semidirect
52. C3×#886C22semidirect
53. C3×#67⋊C4C22semidirect
54. #63978C22semidirect
55. C2×Dic3⋊Dic3C22semidirect
58. C2×#3722C22semidirect
59. C2×#3722C22semidirect
60. C2×#3722C22semidirect
61. C2×#3722C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. #63923C22semidirect
64. D3×(C2×D3)⋊C4C22semidirect
65. #63910C22semidirect
66. #63909C22semidirect
67. #63895C22semidirect
68. #63894C22semidirect
69. #63890C22semidirect
70. #63852C22semidirect
92. C2×#886D3semidirect
100. C2×#67⋊C4D3semidirect
121. C2×#638C23semidirect
126. C2×C4⋊(C3⋊D3)C23semidirect
128. C2×C3×#67D4semidirect
139. C22×C3×Dic3C23semidirect
140. C22×C3×Dic3C23semidirect
142. C2×C3×C4×D3C23semidirect
145. C2×#627C23semidirect
152. C2×#626C23semidirect
153. C2×#626C23semidirect
157. C2×#624C23semidirect
160. C2×D3×Dic3C23semidirect
161. C32×C22⋊C4C23semidirect
163. #3752C23semidirect
164. C3×(C2×D3)⋊C4C23semidirect
165. C3×(C2×D3)⋊C4C23semidirect
166. C3×(C2×D3)⋊C4C23semidirect
167. C3×C4⋊Dic3C23semidirect
168. C3×C4⋊Dic3C23semidirect
169. C3×Dic3⋊C4C23semidirect
170. C3×C4×Dic3C23semidirect
171. Dic3⋊Dic3C23semidirect
174. #3722C23semidirect
175. #3722C23semidirect
176. #3722C23semidirect
177. (C2×D3)⋊Dic3C23semidirect
199. C23×Dic3C2×D3semidirect
200. C23×Dic3C2×D3semidirect
224. C22×C4×D3C2×D3semidirect
236. C2×C3×C22⋊C4C2×D3semidirect
237. C2×C3×C22⋊C4C2×D3semidirect
263. C2×(C2×D3)⋊C4C2×D3semidirect
264. C2×(C2×D3)⋊C4C2×D3semidirect
265. C2×(C2×D3)⋊C4C2×D3semidirect
267. C2×C4⋊Dic3C2×D3semidirect
268. C2×C4⋊Dic3C2×D3semidirect
270. C2×Dic3⋊C4C2×D3semidirect
271. C2×C4×Dic3C2×D3semidirect
279. #886C2×D3semidirect
287. #67⋊C4C2×D3semidirect
308. C22×C3⋊D3#41semidirect
334. C3×#67C2×D4semidirect
447. C2×#67D12semidirect
463. C22×Dic3C22×D3semidirect
464. C22×Dic3C22×D3semidirect
500. C2×C4×D3C22×D3semidirect
512. C3×C22⋊C4C22×D3semidirect
513. C3×C22⋊C4C22×D3semidirect
533. (C2×D3)⋊C4C22×D3semidirect
534. (C2×D3)⋊C4C22×D3semidirect
535. (C2×D3)⋊C4C22×D3semidirect
537. C4⋊Dic3C22×D3semidirect
538. C4⋊Dic3C22×D3semidirect
540. Dic3⋊C4C22×D3semidirect
541. C4×Dic3C22×D3semidirect
562. C2×C3⋊D3C2×#41semidirect
631. C2×C22⋊C4D32semidirect
757. #67C2×D12semidirect
798. C2×C32#546semidirect
879. C22⋊C4C2×D32semidirect
983. C32C2×#546semidirect
1060. C2×C3#5554semidirect
1061. C2×C3#5654semidirect
1119. C3C2×#5554semidirect
1120. C3C2×#5654semidirect
1127. C2#10594293direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#38112
C22×#38042
C2×#640912
C2×C3×#8862
C2×C3×#67⋊C42
C2×#639782
C22×#37222
C2×#639232
C2×D3×(C2×D3)⋊C42
C2×#639102
C2×#639092
C2×#638952
C2×#638942
C2×#638902
C2×#638522
#105942932
C2×#56543
C2×#55543